Find the limit algebraically.
-$$\lim _ { x \rightarrow 0 } \frac { x ^ { 3 } + 12 x ^ { 2 } - 5 x } { 5 x }$$
A) 0
B) $- 1$
C) 5
D) Does not exist

Question

Quizplus · Accepted Answer

To find the limit, simplify the expression: $\frac{x^3 + 12x^2 - 5x}{5x} = \frac{x(x^2 + 12x - 5)}{5x}$. Cancel $x$ from numerator and denominator, resulting in $\frac{x^2 + 12x - 5}{5}$. As $x \to 0$, the expression becomes $\frac{0^2 + 12(0) - 5}{5} = \frac{-5}{5} = -1$.

Find the Limit Algebraically lim⁡x→0x3+12x2−5x5x\lim _ { x \rightarrow 0 } \frac { x ^ { 3 } + 12 x ^ { 2 } - 5 x } { 5 x }x→0lim​5xx3+12x2−5x​

Find the Limit Algebraically $\lim _ { x \rightarrow 0 } \frac { x ^ { 3 } + 12 x ^ { 2 } - 5 x } { 5 x }$